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Academic Genealogy of Shoshichi Kobayashi and Individuals Who Influenced Him

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Academic Genealogy of Shoshichi Kobayashi and Individuals Who Influenced Him Progress in Mathematics, Vol. 308, 17–38 c 2015 Springer International Publishing Academic Genealogy of Shoshichi Kobayashi and Individuals Who Influenced Him Hisashi Kobayashi 1. Introduction Professor Yoshiaki Maeda, a co-editor of this volume, kindly asked me to prepare an article on academic genealogy of my brother Shoshichi Kobayashi. In the olden times, it would have been a formidable task for any individual who is not in the same field as the subject mathematician to undertake a genealogy search. Luck- ily, the “Mathematics Genealogy Project” (administered by the Department of Mathematics, North Dakota State University) [1] and Wikipedia [2] which docu- ment almost all notable mathematicians, provided the necessary information for me to write this article. Before I undertook this study, I knew very little about Shoshichi’s academic genealogy, except for his advisor Kentaro Yano at the Uni- versity of Tokyo and his Ph.D. thesis advisor Carl Allendoerfer at the University of Washington, Seattle. Shoshichi was well versed in the history of mathematics and wrote several tutorial books (in Japanese) (e.g., [3]) and an essay book [4]. In these writings, he emphasized the importance and necessity of studying the history of mathematics in order to really understand why and how some concepts and ideas in mathematics emerged. I am not certain whether Shoshichi was aware that one of his academic ancestors was Leonhard Euler (1707–1783) (see Table 1), whom he immensely admired as one of the three greatest mathematicians in human history. The other two of his choice were Carl Friedrich Gauss (1777–1855) and Archimedes (circa 287 BC–212BC). I was pleasantly surprised to find that his academic ancestry includes not only Euler but also such a large list of celebrated mathematicians, as shown in Table 1: Gottfried Leibniz (1646–1716), Jacob Bernoulli (1655–1705), Johann Bernoulli (1667–1748), Jean d’Alembert (1717–1783), Joseph Lagrange (1736–1813), Pierre- Simon Laplace (1749–1827) and Simeon Poisson (1781–1840). In Section 2, I will summarize what I have found about some of the older ancestors of Shoshichi: Gottfried Leibniz, Nicolas Malebranche, Jacob Bernoulli, Johann Bernoulli and Leonhard Euler. It goes without saying that we would learn a great deal also by studying d’Alembert, Lagrange, Laplace and Poisson,allof 18 H. Kobayashi Gottfried Wilhelm Leibniz (1666, Universität Leipzig) ? Nicolas Malebranche (1672, school unknown) Jacob Bernoulli (1684, Universität Basel) Johann Bernoulli (1694, Universität Basel) Leonhard Euler (1726, Universität Basel) Jean Le Rond d'Alembert Joseph Louis Lagrange Pierre-Simon Laplace Simeon Denis Poisson (1800, École Polytechnique) Michel Chasles (1814, École polytechnique) Hubert Anson Newton (1885, Yale Univerity) Eliakim Hastings Moore (1885, Yale University) Oswald Veblen (1903, University of Chicago) Tracy Yerkes Thomas (1923, Princeton University) Carl Barnett Allendoerfer (1937, Princeton University) Shoshichi Kobayashi (1956, University of Washington) Table 1. Shoshichi Kobayashi’s Academic Ancestry whom are household names, so to speak, to all scientists and engineers. But in the interest of space, I should find another opportunity to discuss these mathemati- cians. In Section 3, I will make another important account of various individu- als with whom Shoshichi interacted directly, although they do not appear in Shoshichi’s genealogical tree of Table 1. Academic Genealogy of Shoshichi Kobayashi 19 2. Some Great Mathematicians among Shoshichi’s Academic Ancestry As stated earlier, Table 1 provides an important segment of Shoshichi Kobayashi’s academic ancestry. At the top of Table 1 is Gottfried Wilhelm Leibniz (1646–1716), a prominent German mathematician and philosopher [5, 6]. Gottfried Leibniz developed the theory of differentiation and integration, independently of his contemporary, Isaac Newton (1642–1727) (see the Leibniz– Newton controversy on calculus [7]) and Leibniz’ no- tation for infinitesimal calculus has been widely used ever since it was introduced [4] (pp. 46–48). His Ph.D. thesis at age 20 (in 1666) was on “Disputa- tio arithmetica de complexionibus (Arithmetic dis- cussion of combinations)” under two advisors (not shown in Table 1) at the University of Leipzig: Jakob Thomasius (1622–1684), a philosopher, and Er- hard Weigel (1625–1699), a mathematician and as- tronomer. Thomasius’ advisor was Friedrich Leibniz (1597–1652), the father of Gottfried Leibniz, a profes- sor of philosophy at Leipzig. Gottfried’s other advisor Weigel was an academic descendant of Nicolas Coper- nicus (1473–1543) (not shown in Table 1). Gottfried Wilhelm von During his stay in France around 1670, Leibniz Leibniz (1646–1716) met the Dutch physicist and mathematician Christian Source: http://www- Huygens (1629–1695). With him as mentor, Leibniz history.mcs.st-and.ac.uk/. made major contributions, including the discovery of Public domain. differential and integral calculus. According to the Mathematics Genealogy Project [6], Leibniz submitted another dissertation to Acad´emie Royale des sciences de Paris in 1676 with Huygens as the advisor, although the type of degree is not given. Thus, we may claim Huygens as a mathematical ancestor of Shoshichi. Nicolas Malebranche (1638–1715) was a French Oratorian priest and ratio- nalist philosopher. The Mathematics Genealogy Project shows Malebranche as one of Leibniz’s two students [6], but neither his dissertation title nor his university is given. In Wikipedia [8] no mention is made regarding the advisor-student rela- tionship between Malebranche and Leibniz, but their collaboration on physics and mathematics is briefly mentioned. Considering that Malebranche was eight years senior to Leibniz, it is quite possible that Malebranche was not an official student of Leibniz, but he learned mathematics and physics from Leibniz. We need more investigation to prove the genealogy link between the two. Malebranche intro- duced Guillaume de l’Hˆopital (1661–1704) to Johann Bernoulli (see a paragraph below regarding an unusual contract and dispute between l’Hˆopital and Johann Bernoulli). Jacob Bernoulli (1654–1705) [9] was the first mathematician in the famous Bernoulli family, of which Shoshichi gives a full account in Chapter “Mathe- matical families” (pp. 30–39) of [4] as well as in Section 4.1 (pp. 167–171) of 20 H. Kobayashi “Chapter 4: Euler” of his book on Fermat and Euler [3]. Jacob made numer- ous contributions, and is well known, among other things, for the calculus of variations and the Bernoulli numbers. The Bernoulli numbers appear in various mathematical fields. Those who study probability theory (see, e.g., [10] which I recently published) learn the work of Ja- cob Bernoulli through Bernoulli’s Theorem (a.k.a. the weak law of large numbers), Bernoulli trials, Bernoulli distributions, etc. In 1657, the aforementioned Chris- tian Huygens published the first book on probability entitled De Ratiociniis in Ludo Aleae (On Reasoning in Games of Chance), a treatise on problems asso- ciated with gambling, motivated by Pascal and Fer- Jacob Bernoulli (1654– mat’s correspondence (see, e.g., [10]). Huygens’ book 1705) Source: Wikipedia. influenced Jacob Bernoulli who worked on probabil- Public domain. ity theory around 1684–1689. Much of Jacob’s work is found in his book Ars Conjectandi (The Art of Conjecture), published posthu- mously in 1713 by his nephew Nicholas Bernoulli (1687–1759). Johann Bernoulli (1667–1748) [11] who was 13 years younger than Jacob, studied mathematics from Jacob. Throughout Johann’s education at the Univer- sity of Basel, the Bernoulli brothers worked together on the newly discovered infinitesimal calculus. Shortly after the graduation of Johann, however, the two developed a jealous and competitive relationship [4, 11]. After Jacob’s death, Johann’s jealousy shifted to- wards his own talented son, Daniel Bernoulli (1700– 1782). Johann Bernoulli, introduced by Malebranche, was hired by l’Hˆopital for tutoring in mathematics. In 1694, l’Hˆopital made an unusual contract with Johann Bernoulli [4, 12] in exchange for an annual payment of 300 Francs that Johann would inform Johann Bernoulli l’Hˆopital of his latest mathematical discoveries. Two (1667–1748) Source: years later l’Hˆopital authored the first textbook on Wikipedia. Public infinitesimal calculus, Analyse des Infiniment Petits domain. pour l’Intelligence des Lignes Courbes (Analysis of the infinitely small to understand curves), including what is now known as l’Hˆopital’s rule. After l’Hˆopital’s death, Johann publicly revealed their agreement and claimed credit for portions of the text of Analyse. For a long time, however, his claims were not regarded as credible by many historians and mathematicians, because Johann had been previously involved in several disputes with his brother Jacob and his own son Daniel. In 1921, however, Paul Schafheitlin [13] discovered a manuscript of Johann’s lectures on differential calculus written during 1691–1692, substantiating Bernoulli’s account of the book’s origin. Academic Genealogy of Shoshichi Kobayashi 21 Leonhard Euler’s (1707–1783) father Paul Euler was a pastor, who studied in his youth mathematics from Jacob Bernoulli, and thus was a friend of the Bernoulli family. Leonhard studied mathemat- ics from Johann Bernoulli and be- came a close friend of Johann’s sons Nicholas and Daniel. In 1725 Daniel Bernoulli was appointed the chairman of the mathematics/physics division of the St. Petersburg Academy of Sci- ences (today’s Russian Academy of Sciences), established that year by Pe- ter the Great who had consulted with Leibniz. Upon Daniel’s recommenda- tion, Euler was appointed to a posi- tion of physiology at the Academy in 1727 at age 20, and became a profes- sor of physics in 1731. In 1733, Daniel Bernoulli returned to the University of Basel and Leonhard took over Daniel’s position as the head of the mathe- matics department at the Academy. In 1735 (age 28) he suffered a near-fatal Leonhard Euler (1707–1783). Source: Wikipedia. Portrait of Leonhard Euler fever and became almost blind in his painted by Jakob Emanuel Handmann right eye, but continued to be produc- (1718–1781).
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